On High-Resolution Head-Related Transfer Function Measurements: An Efficient Sampling Scheme

This paper deals with two important questions associated with HRTF measurement: 1) “what is the required angular resolution?,” and 2) “what is the most suitable sampling scheme?.” The paper shows that a well-defined finite number of spherical harmonics can capture the head-related transfer function (HRTF) spatial variations in sufficient detail, which is defined as the HRTF spatial dimensionality. For the 20-kHz audible frequency range, the value of the dimensionality means a high-directional resolution HRTF measurement is required. Considering such a high-resolution measurement, a number of sampling criteria have been identified from both mechanical setup and data processing aspects. Different sampling candidates are then compared to demonstrate that the best method which satisfies all requirements is the class termed as IGLOO. A fast spherical harmonic transform algorithm based on the IGLOO scheme is developed to accelerate the high-resolution data analysis. The proposed method is validated through simulation and experimental data acquired from a KEMAR mannequin.

[1]  R. Duraiswami,et al.  Insights into head-related transfer function: Spatial dimensionality and continuous representation. , 2010, The Journal of the Acoustical Society of America.

[2]  Paul N. Swarztrauber,et al.  On Computing the Points and Weights for Gauss-Legendre Quadrature , 2002, SIAM J. Sci. Comput..

[3]  John G. Proakis,et al.  Digital Signal Processing: Principles, Algorithms, and Applications , 1992 .

[4]  Xiaoli Zhong,et al.  Maximal azimuthal resolution needed in measurements of head-related transfer functions. , 2009, The Journal of the Acoustical Society of America.

[5]  K. Gorski,et al.  HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere , 2004, astro-ph/0409513.

[6]  R. Kress,et al.  Inverse Acoustic and Electromagnetic Scattering Theory , 1992 .

[7]  Jens Blauert,et al.  The AUDIS catalog of human HRTFs , 1998 .

[8]  F L Wightman,et al.  Headphone simulation of free-field listening. I: Stimulus synthesis. , 1989, The Journal of the Acoustical Society of America.

[9]  W. G. Gardner,et al.  HRTF measurements of a KEMAR , 1995 .

[10]  R. Duraiswami,et al.  Plane-wave decomposition analysis for spherical microphone arrays , 2005, IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2005..

[11]  Jacob Benesty,et al.  Audio Signal Processing for Next-Generation Multimedia Communication Systems , 2004 .

[12]  Anthony I. Tew,et al.  Analyzing head-related transfer function measurements using surface spherical harmonics , 1998 .

[13]  Martin Vetterli,et al.  Plenacoustic function on the circle with application to HRTF interpolation , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[14]  Rodney A. Kennedy,et al.  Modal expansion of HRTFs: Continuous representation in frequency-range-angle , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[15]  Flemming Christensen,et al.  Directional resolution of head-related transfer functions required in binaural synthesis , 2005 .

[16]  Larry S. Davis,et al.  Rendering localized spatial audio in a virtual auditory space , 2004, IEEE Transactions on Multimedia.

[17]  Michael P. Hobson,et al.  Fast Directional Continuous Spherical Wavelet Transform Algorithms , 2005, IEEE Transactions on Signal Processing.

[18]  Ramani Duraiswami,et al.  Regularized HRTF fitting using spherical harmonics , 2009, 2009 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics.

[19]  Mark A. Wieczorek,et al.  Spatiospectral Concentration on a Sphere , 2004, SIAM Rev..

[20]  Robert G. Crittenden,et al.  Exactly azimuthal pixelizations of the sky , 1998 .

[21]  Michael Friis Sørensen,et al.  Head-Related Transfer Functions of Human Subjects , 1995 .

[22]  Jörg Fliege,et al.  The distribution of points on the sphere and corresponding cubature formulae , 1999 .

[23]  Thushara D. Abhayapala,et al.  Spherical Harmonic Analysis of Wavefields Using Multiple Circular Sensor Arrays , 2010, IEEE Transactions on Audio, Speech, and Language Processing.

[24]  Ramani Duraiswami,et al.  INTERPOLATION AND RANGE EXTRAPOLATION OF HRTFS , 2004 .

[25]  C. Avendano,et al.  The CIPIC HRTF database , 2001, Proceedings of the 2001 IEEE Workshop on the Applications of Signal Processing to Audio and Acoustics (Cat. No.01TH8575).

[26]  William L. Martens,et al.  Principal Components Analysis and Resynthesis of Spectral Cues to Perceived Direction , 1987, ICMC.

[27]  D. M. Green,et al.  Directional sensitivity of sound-pressure levels in the human ear canal. , 1989, The Journal of the Acoustical Society of America.

[28]  D. Healy,et al.  Computing Fourier Transforms and Convolutions on the 2-Sphere , 1994 .

[29]  Xiaoping Chen,et al.  Measuring the head-related transfer functions of an artificial head with a high directional resolution , 2000 .

[30]  Christof Faller,et al.  Sound Field Analysis along a Circle and Its Applications to HRTF Interpolation , 2008 .

[31]  R. Duda,et al.  Range dependence of the response of a spherical head model , 1998 .

[32]  Rodney A. Kennedy,et al.  Intrinsic Limits of Dimensionality and Richness in Random Multipath Fields , 2007, IEEE Transactions on Signal Processing.

[33]  Rodney A. Kennedy,et al.  Characterization of 3D spatial wireless channels , 2003, 2003 IEEE 58th Vehicular Technology Conference. VTC 2003-Fall (IEEE Cat. No.03CH37484).

[34]  Ramani Duraiswami,et al.  Flexible and Optimal Design of Spherical Microphone Arrays for Beamforming , 2007, IEEE Transactions on Audio, Speech, and Language Processing.

[35]  Rodney A. Kennedy,et al.  HRTF Measurement on KEMAR Manikin , 2009 .

[36]  E. Shaw The External Ear , 1974 .

[37]  Tianshu,et al.  Head-related Transfer Function Measurement , 2013 .